Despite its long history and stunning experimental successes, the mathematical foundation of perturbative quantum field theory is still a subject of ongoing research.
This book aims at presenting some of the most recent advances in the field, and at reflecting the diversity of approaches and tools invented and currently employed.
Both leading experts and comparative newcomers to the field present their latest findings, helping readers to gain a better understanding of not only quantum but also classical field theories. Though the book offers a valuable resource for mathematicians and physicists alike, the focus is more on mathematical developments.
This volume consists of four parts:
The first Part covers local aspects of perturbative quantum field theory, with an emphasis on the axiomatization of the algebra behind the operator product expansion. The second Part highlights Chern-Simons gauge theories, while the third examines (semi-)classical field theories. In closing, Part 4 addresses factorization homology and factorization algebras.
Author(s): Damien Calaque, Thomas Strobl (eds.)
Series: Mathematical Physics Studies
Edition: 1
Publisher: Springer International Publishing
Year: 2015
Language: English
Pages: 556
Tags: Quantum Field Theories, String Theory; Mathematical Physics; History and Philosophical Foundations of Physics; Mathematical Applications in the Physical Sciences
Front Matter....Pages i-xxviii
A Derived and Homotopical View on Field Theories....Pages 1-14
Front Matter....Pages 15-15
Perturbative Algebraic Quantum Field Theory....Pages 17-55
Lectures on Mathematical Aspects of (twisted) Supersymmetric Gauge Theories....Pages 57-87
Snapshots of Conformal Field Theory....Pages 89-129
Front Matter....Pages 131-131
Faddeev’s Quantum Dilogarithm and State-Integrals on Shaped Triangulations....Pages 133-152
A Higher Stacky Perspective on Chern–Simons Theory....Pages 153-211
Factorization Homology in $$3$$ 3 -Dimensional Topology....Pages 213-231
Deligne-Beilinson Cohomology in U(1) Chern-Simons Theories....Pages 233-271
Front Matter....Pages 273-273
Semiclassical Quantization of Classical Field Theories....Pages 275-324
Local BRST Cohomology for AKSZ Field Theories: A Global Approach....Pages 325-341
Symplectic and Poisson Geometry of the Moduli Spaces of Flat Connections Over Quilted Surfaces....Pages 343-411
Groupoids, Frobenius Algebras and Poisson Sigma Models....Pages 413-426
Front Matter....Pages 427-427
Notes on Factorization Algebras, Factorization Homology and Applications....Pages 429-552
Back Matter....Pages 553-556
